## Theory about Scientific Notation

# Scientific Notation

**Scientific Notation** helps us to express in an easier way those numerical quantities that are too large or, conversely, too small.

It is also known as Exponential Notation and it can be defined as the product of a number that is in the range of 1 to 10, multiplied by the power of 10.

A number written in scientific notation consists of:

- A whole part that is formed by a single number which is not zero.
- The other significant numbers, if there is, set as decimal part.
- A power base 10 gives the order of the number magnitude.

If *n* is positive, the number N is “large”. And if *n* is negative, then N is “small”

To express a number in scientific notation we must identify the decimal point (if there is) and move it to the left if the number to be converted is greater than 10, however, if the number is less than 1 (start with zero and coma) we move it to the right as many places as it is necessary so that (in both cases) the only digit that is to the left side of the decimal point is between 1 and 9 and all others digits that appear to the right of the decimal point.

Only are selected the integer numbers because mathematically the zeros do not exist and they should not be included.

For example:

**Operations with numbers in Scientific Notation:**

If we have an addition or subtraction (or both of them) with expressions in scientific notation, the first thing to do is factored, using as factor the smallest of the powers of 10 and factor it. Then we need to fix the result to put it in scientific notation.__Addition and Subtraction:__

To perform a multiplication we have to multiply decimals of scientific notations and then we have to apply the product of powers for the powers of base 10 (adding the exponents)__Multiplications:__

decimal expressions of scientific notations are divided and then we have to apply the division of powers to the power of base 10. If it its necessary, adjust the result as a new scientific notation.__Divisions:__

If we have any scientific notation raised to an exponent, we have to raise the integer number to the power that is told us and then we have to multiply the exponents of power 10, to be so the power raised.__Powers:__

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